## Psi used in auto-logistic model

questions concerning analysis/theory using program PRESENCE

### Psi used in auto-logistic model

I have a pretty straightforward if technical question... What exactly does PRESENCE do to calculate the annual psi estimate used in the auto-logistic term? I've read both the PRESENCE help document, and the original Yackulic et al. 2012 & Eaton et al. 2014 papers & supplements that the model was created for AFAIK, and neither clearly states the formulae used.

The help file gives the example:

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`Xsite4,t-1 = (Wsite3 * ψsite3,t-1 + Wsite5 * ψsite5,t-1) / (Wsite3 + Wsite5 )`

Are the ψ in this case unconditional psi (modeled probability only) or conditional psi (taking into account the actual detection history at that site in that year)? The papers discuss that conditional can be used, but the above help file example reads like it's just the general probability of occupancy (i.e., the unconditional psi derived parameter). If this is conditional psi, how exactly is this calculated within PRESENCE?

nathanvs

Posts: 6
Joined: Fri Nov 20, 2015 5:07 pm

### Re: Psi used in auto-logistic model

Sorry for the confusion. PRESENCE will use conditional occupancy if 'psi1' is in the design matrix for gam or eps. To use unconditional occupancy, enter 'upsi1' in the design matrix. I'll update the documentation.
jhines

Posts: 401
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

### Re: Psi used in auto-logistic model

Thanks for the reply, that's quite helpful! I was also wondering, how is conditional occupancy calculated for psi1? Is this correct?

Detected: 1
Undetected: [derived annual psi] * (1-p) ^ [# surveys]

Thanks again,
Nathan
nathanvs

Posts: 6
Joined: Fri Nov 20, 2015 5:07 pm

### Re: Psi used in auto-logistic model

Conditional occupancy is computed as:

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`               Psi * Prod(1-p(j))Psi-c = ---------------------------------------            1-Psi + Psi*Prod(1-p(j))`

where Prod(1-p(j)) = (1-p(1))*(1-p(2))*(1-p(3))*...(1-p(K))
jhines

Posts: 401
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA